## SOFR Rate Curve

### FinPricing offers:

#### Four user interfaces:

**Data API**.**Excel Add-ins**.**Model Analytic API**.**GUI APP.**

**Data API**.**Excel Add-ins**.**Model Analytic API**.**GUI APP.**

FinPricing offers the following curve data for various currencies via API. All the interest rate curves have data points up to 50 years.

- OIS curves
- RFR (risk free rate) curves
- SOFR, €STR (ESTR, ESTER), SONIA, TONA, CORRA, AONIA, SARON rate curves
- IBORs (LIBOR, EURIBOR, TIBOR, CDOR, EONIA, etc.) fallback rate curves
- Swap rate curves
- Basis curves
- Spot rate or zero rate curves
- Forward rate curves
- Discount curves
- Inflation Swap rate (CPI, RPI, HICP) curves
- Nordic electricity futures curve
- VIX futures curve
- S&P 500 futures curve

1. SOFR Curves |

FinPricing provides the following SOFR rates:

**SOFR Rate**: Secured Overnight Financing Rate**EFFR Rate**: Effective Federal Funds Rate**OBFR Rate**: Overnight Bank Funding Rate**BGCR Rate**: Broad General Collateral Ratee**TGCR Rate**: Tri-Party General Collateral Rate**SOFR Average Rates**: 30-day average, 90-day average, and 180-day average**SOFR Index**: Cumulative impact of compounding the SOFR**SOFR Term Curve**: SOFR term curve or SOFR spot curve is derived from the SOFR derivatives markets. Unlike the other SOFR rates above, it is forward-looking and is developed based on actual SOFR future transactions (SOFR futures and SOFR swaps). Our curve is very accurate and granular, and up to 50 years.**SOFR Discount Rate/Factor Curve**: SOFR discount factor curve is also forward-looking and is developed based on actual SOFR future transactions (SOFR futures and SOFR swaps). The curve we offer is very accurate and granular, and up to 50 years.**SOFR Forward Curves**: SOFR forward curves are also forward-looking and are developed based on actual SOFR future transactions (SOFR futures and SOFR swaps). Our curves are very accurate and granular, and up to 50 years.**SOFR Swap Curve**

The SOFR Index measures the cumulative impact of compounding the SOFR on a unit of investment over time, with the initial value set to 1.0 on April 2, 2018, the first value date of the SOFR. The SOFR Index reflects the effect of compounding the SOFR each business day and allows the calculation of compounded SOFR averages over custom time periods.

The SOFR Average rates are an extension of the Secured Overnight Financing Rate (SOFR). They are compounded averages of the SOFR over rolling 30-, 90-, and 180-calendar day periods. Many consumer loans,corporation loans, and retail debts will use SOFR compounded in advance, which is calculated by compounding interest over a previous set number of days.

A SOFR forward curve is the term structure of forward SOFR rates at different forward starting dates and forward periods, while a spot SOFR term curve is the term structure of spot SOFR term rates and their maturities. SOFR foward rates are used to forecast interest payments or cash flows in future.

Spot SOFR term rates are implied by SOFR derivatives, such as SOFR futures and SOFR swap rates. Those SOFR derivatives are forword-looking, reflecting market expectations of SOFR rates in future.

FinPricing provides near real-time SOFR swap curve and 1-month, 2-month, 3-month, 4-month, 5-month, 6-month, 7-month, 8-month, 9-month, 10-month, 11-month, and 12-month SOFR forward curves, as well as spot SOFR term and discount curves with high accuracy. Each curve has data points up to 50 years. Users can specify any forward intervals and forward periods/terms.

Most commonly used SOFR forward curves are 1-month, 3-month, and 6-month curves shown below (each curve has tenors up to 50 years, too long to display all here):

Valuation Date | Forward Date | 1M SOFR Forward Rate | 3M SOFR Forward Rate | 6M SOFR Forward Rate |
---|---|---|---|---|

2023-01-10 | 2023-02-10 | 4.705220087 | 4.84080669 | 4.947191567 |

2023-01-10 | 2023-03-10 | 4.832302312 | 4.935521839 | 4.98323335 |

2023-01-10 | 2023-04-10 | 4.920093847 | 4.993891679 | 5.003319825 |

2023-01-10 | 2023-05-10 | 4.993361191 | 4.991191325 | 4.972991696 |

2023-01-10 | 2023-06-10 | 5.005813611 | 4.968930278 | 4.923642988 |

2023-01-10 | 2023-07-10 | 4.913189417 | 4.950983262 | 4.868068905 |

2023-01-10 | 2023-08-10 | 4.92784026 | 4.893234548 | 4.761389188 |

2023-01-10 | 2023-09-10 | 4.951233238 | 4.817519354 | 4.637926638 |

2023-01-10 | 2023-10-10 | 4.743212156 | 4.726173724 | 4.493698714 |

2023-01-10 | 2023-11-10 | 4.702485855 | 4.573138421 | 4.370046133 |

2023-01-10 | 2023-12-10 | 4.676737425 | 4.405419304 | 4.239638367 |

2023-01-10 | 2024-01-10 | 4.292581419 | 4.208532678 | 4.097815647 |

2023-01-10 | 2024-02-10 | 4.185835899 | 4.115005753 | 3.968951898 |

2023-01-10 | 2024-03-10 | 4.102788149 | 4.031379262 | 3.841515807 |

2023-01-10 | 2024-04-10 | 4.017653909 | 3.945694395 | 3.708437658 |

2023-01-10 | 2024-05-10 | 3.932967536 | 3.787639525 | 3.571525698 |

2023-01-10 | 2024-06-10 | 3.847863767 | 3.614939919 | 3.430085794 |

2023-01-10 | 2024-07-10 | 3.548478392 | 3.439940273 | 3.285620702 |

2023-01-10 | 2024-08-10 | 3.423590645 | 3.323700743 | 3.240059035 |

2023-01-10 | 2024-09-10 | 3.314361984 | 3.213896362 | 3.209385985 |

USD SOFR Term Curve:

Valuation Date | Curve Name | Maturity | Spot Rate |
---|---|---|---|

2023-01-16 | USD.SOFR | 2023-04-16 | 4.658072554 |

2023-01-16 | USD.SOFR | 2023-07-16 | 4.801509197 |

2023-01-16 | USD.SOFR | 2023-10-16 | 4.839151738 |

2023-01-16 | USD.SOFR | 2024-01-16 | 4.799990052 |

2023-01-16 | USD.SOFR | 2024-04-16 | 4.667001481 |

2023-01-16 | USD.SOFR | 2024-07-16 | 4.532976822 |

2023-01-16 | USD.SOFR | 2024-10-16 | 4.357655424 |

2023-01-16 | USD.SOFR | 2025-01-16 | 4.181896423 |

2023-01-16 | USD.SOFR | 2025-04-16 | 4.067678383 |

2023-01-16 | USD.SOFR | 2025-07-16 | 3.953885663 |

2023-01-16 | USD.SOFR | 2025-10-16 | 3.838838554 |

2. SOFR Curve Introduction |

LIBOR was a daily calculated and globally accepted benchmark interest rate. However, an investigation revealed international banks had been manipulating LIBOR for profit for many years. Due to the erosion of public trust, LIBOR experienced a decline in its trust as a benchmark interest rate.

The manipulation scandal with LIBOR, EURIBOR and TIBOR undermined confidence in the reliability and robustness of major reference rates. In the Euro area, €STR was recommended as risk-free rate (RFR) in order to replace the Euro Overnight Index Average (EONIA)

The Alternative Rates Reference Committee (ARRC) recommended the adoption of Secured Overnight Financing Rate (SOFR) rates as a recommended alternative to LIBOR. Consequently, US Fed announced that 1-week and 2-month USD LIBOR will be last published on 31 December 2021 but 1-month, 3-month, 6-month, 12-month USD LIBOR settings will continue till 30 June 2023.

Similarly, all Sterling, Euro, Swiss franc and Japanese yen LIBOR settings will cease immediately after 31 December 2021, although 1-month, 3-month and 6-month GBP and JPY LIBOR will be published under a new “synthetic” methodology for 2022

The European Central Bank (ECB) published the daily publication of €STR as overnight rate on 2 October 2019. From 14 April 2021 the ECB started publication of backward-looking €STR-based term rates, called Compounded €STR average rates.

SOFR was a daily rate that meant it could not act as a viable replacement rate for LIBOR. To replace LIBOR with a daily rate would require substantial changes in the way interest rates are calculated and reported. Therefore, Term SOFR came to light as a viable replacement to LIBOR.

Since term SOFR is determined “in advance”, it requires less of a change for syndicated and bilateral loan facilities than other SOFR rates. In general, term SOFR works similarly to that of LIBOR and will serve as a capable replacement.

Some of the key factors for choosing risk-free rates were the depth of liquidity, volatility, practical usage, and the Principles of interest rate benchmarks. As a result, several alternative overnight rates are recommended:

- Secured Overnight Financing Rate (SOFR) for USD
- Sterling Overnight Index Average (SONIA) for GBP
- Euro short-term rate (€STR) for EUR,
- Swiss Average Rate Overnight (SARON) for CHF
- Tokyo Overnight Average Rate (TONA or TONAR) for JPY

3. SOFR Curve Construction and Bootstrapping Overview |

The term structure of a SOFR curve is constructed from a set of market quotes of some liquid market instruments. Normally a SOFR curve is divided into two parts. The short end of the term structure is determined using deposit rates. The remaining is derived using swap rates.

The objective of the bootstrap algorithm is to find the zero yield or discount factor for each maturity point and
cash flow date sequentially so that all curve instruments can be priced back to the market quotes. All
bootstrapping methods build up the term structure from shorter maturities to longer ones. The output of the construction
process is the zero rate curves.

First you need to construct the base yield curve as guided at yield curve construction.

Assuming that we have had all the yields of a 6-month swap curve data up to 4 years and now need to derive up to 5 years.

- Let x be the yield at 5 years.
- Use an interpolation method to get yields at 4.5 years as Ax
- Given the 5 year swap rate, we can use a root-finding algorithm to solve the x that makes the value of the 5 year inception swap equal to zero.
- Now we obtain all yields or equivalent discount factors up to 5 years

Repeat the above procedure till the longest swap maturity.

There are two keys in yield curve construction: interpolation and optimization for root
finding.

4. Interpolation |

Most popular interpolation algorithms in curve bootstrapping are linear, log-linear and cubic spline. They can be
applied to either zero rates or discount factors.

Some critics argue that some of those simple interpolations cannot generate smooth forward rates and the others may
be able to produce smooth forward rates but fail to match the market quotes. Also they cannot guarantee the continuity
and positivity of forward rates.

The monotone convex interpolation is more rigorous. It meets the following essential criteria:

- Replicate the quotes of all input underlying instruments.
- Guarantee the positivity of the implied forward rates
- Produce smooth forward curves.

Although the monotone convex interpolation rule sounds almost perfectly, it is not very popular with market
practitioners.

5. Optimization |

As described above, the bootstrapping process needs to solve a yield using a root finding algorithm. In other words,
it needs an optimization solution to match the prices of curve-generated instruments to their market quotes.

FinPricing employs the Levenberg-Marquardt algorithm for root finding, which is very common in curve construction.
Another popular algorithm is the Excel Solver, especially in Excel application.

6. Related Topics |